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D.4.31.2 realzero
Procedure from library realrad.lib (see realrad_lib).
- Usage:
- realzero(j); a zero-dimensional ideal j
- Return:
- j: a zero dimensional ideal, which is the real radical
of i, if dim(i)=0
0: otherwise
this acts via
primary decomposition (i=1)
listdecomp (i=2) or facstd (i=3)
Example:
| | LIB "realrad.lib";
//in non parametric fields
ring r=0,(x,y),dp;
ideal i=(y3+3y2+y+1)*(y2+4y+4)*(x2+1),(x2+y)*(x2-y2)*(x2+2xy+y2)*(y2+y+1);
realzero(i);
==> _[1]=y4+5y3+7y2+3y+2
==> _[2]=x4-x2y2+x2y-y3
ideal j=(y3+3y2+y+1)*(y2-2y+1),(x2+y)*(x2-y2);
realzero(j);
==> _[1]=y4+2y3-2y2-1
==> _[2]=x2y3+3x2y2+x2y-y3+x2-3y2-y-1
==> _[3]=x4-x2y2+x2y-y3
//to get every path
ring r1=(0,t),(x,y),lp;
ideal m1=x2+1-t,y3+t2;
ideal m2=x2+t2+1,y2+t;
ideal m3=x2+1-t,y2-t;
ideal m4=x^2+1+t,y2-t;
ideal i=intersect(m1,m2,m3,m4);
realzero(i);
==> _[1]=y5+(-t)*y3+(t2)*y2+(-t3)
==> _[2]=x2+(-t+1)
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